Calculating with standard form

The Maths Habit

  1. Write 0.00052 in standard form.

    5.2 × 10−4

  2. Write 3.9 × 10−2 as an ordinary number.

    0.039

  3. Which is smaller: 7 × 10−3 or 2.5 × 10−2?

    7 × 10−3 (0.007)

Sam says 3000 × 2000 = 600 000.
Is Sam right?

No: it is 6 000 000

Write as a single power of 10

  1. 103 × 105

    108

  2. 107 ÷ 103

    104

  3. 104 × 106

    1010

  4. 109 ÷ 108

    101

Write in standard form

24 × 108 2.4 × 10 × 108 = 2.4 × 109

Work out (3 × 105) × (2 × 106)
Give your answer in standard form.

the numbersthe powers of 10
3 × 2 = 6105 × 106 = 1011
put them back together. Is it standard form?
6× 1011
Answer6 × 1011

Work out (5 × 107) × (4 × 103)
Give your answer in standard form.

the numbersthe powers of 10
5 × 4 = 20107 × 103 = 1010
put them back together. Is it standard form?
20× 1010
Answer2 × 1011

Work out (3 × 105) × (2 × 106)
Give your answer in standard form.

the numbersthe powers of 10
3 × 2 = 6105 × 106 = 1011
put them back together. Is it standard form?
6× 1011
Answer6 × 1011

Work out (7 × 103) × (2 × 105)
Give your answer in standard form.

the numbersthe powers of 10
7 × 2 = 14103 × 105 = 108
put them back together. Is it standard form?
14× 108
Answer1.4 × 109

Work out (6 × 109) ÷ (2 × 104)
Give your answer in standard form.

the numbersthe powers of 10
6 ÷ 2 = 3109 ÷ 104 = 105
put them back together. Is it standard form?
3× 105
Answer3 × 105

Work out (9 × 1010) ÷ (3 × 106)
Give your answer in standard form.

the numbersthe powers of 10
9 ÷ 3 = 31010 ÷ 106 = 104
put them back together. Is it standard form?
3× 104
Answer3 × 104

Work out (6 × 109) ÷ (2 × 104)
Give your answer in standard form.

the numbersthe powers of 10
6 ÷ 2 = 3109 ÷ 104 = 105
put them back together. Is it standard form?
3× 105
Answer3 × 105

Work out (8 × 109) ÷ (4 × 105)
Give your answer in standard form.

the numbersthe powers of 10
8 ÷ 4 = 2109 ÷ 105 = 104
put them back together. Is it standard form?
2× 104
Answer2 × 104

Work out (3 × 105) × (2 × 106)
Give your answer in standard form.

the numbersthe powers of 10
3 × 2 = 6105 × 106 = 1011
put them back together. Is it standard form?
6× 1011
Answer6 × 1011

Work out (1.5 × 104) × (3 × 106)
Give your answer in standard form.

the numbersthe powers of 10
1.5 × 3 = 4.5104 × 106 = 1010
put them back together. Is it standard form?
4.5× 1010
Answer4.5 × 1010

Work out (6 × 109) ÷ (2 × 104)
Give your answer in standard form.

the numbersthe powers of 10
6 ÷ 2 = 3109 ÷ 104 = 105
put them back together. Is it standard form?
3× 105
Answer3 × 105

Work out (8.4 × 109) ÷ (2 × 103)
Give your answer in standard form.

the numbersthe powers of 10
8.4 ÷ 2 = 4.2109 ÷ 103 = 106
put them back together. Is it standard form?
4.2× 106
Answer4.2 × 106

Work out (3 × 105) × (2 × 106)
Give your answer in standard form.

the numbersthe powers of 10
3 × 2 = 6105 × 106 = 1011
put them back together. Is it standard form?
6× 1011
Answer6 × 1011

Work out (6 × 102) × (8 × 104)
Give your answer in standard form.

the numbersthe powers of 10
6 × 8 = 48102 × 104 = 106
put them back together. Is it standard form?
48× 106
Answer4.8 × 107

Calculating with standard form worksheet, page 1

Answer sheet

  1. Light travels 3 × 105 km each second. How far does it travel in 2 × 103 seconds?

    6 × 108 km

  2. A grain of sand has a mass of 4 × 10−3 g. Find the mass of 5 × 106 grains.

    2 × 104 g

  1. Work out (3 × 104) × (2 × 105)

    6 × 109

  2. Work out (8 × 109) ÷ (2 × 103)

    4 × 106

  3. Work out (6 × 105) × (5 × 102). Give your answer in standard form.

    3 × 108
Exit tickets to print